TSTP Solution File: SWC182+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC182+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:54:18 EDT 2023
% Result : Theorem 24.12s 3.44s
% Output : Proof 24.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC182+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 16:31:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 24.12/3.44 Command-line arguments: --flatten
% 24.12/3.44
% 24.12/3.44 % SZS status Theorem
% 24.12/3.44
% 24.18/3.47 % SZS output start Proof
% 24.18/3.47 Take the following subset of the input axioms:
% 24.18/3.48 fof(ax16, axiom, ![U]: (ssList(U) => ![V]: (ssItem(V) => ssList(cons(V, U))))).
% 24.18/3.48 fof(ax2, axiom, ?[U2]: (ssItem(U2) & ?[V2]: (ssItem(V2) & U2!=V2))).
% 24.18/3.48 fof(ax26, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ssList(app(U2, V2))))).
% 24.18/3.48 fof(ax28, axiom, ![U2]: (ssList(U2) => app(nil, U2)=U2)).
% 24.18/3.48 fof(ax39, axiom, ~singletonP(nil)).
% 24.18/3.48 fof(ax4, axiom, ![U2]: (ssList(U2) => (singletonP(U2) <=> ?[V2]: (ssItem(V2) & cons(V2, nil)=U2)))).
% 24.18/3.48 fof(ax45, axiom, ![U2]: (ssList(U2) => frontsegP(U2, nil))).
% 24.18/3.48 fof(ax5, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => (frontsegP(U2, V2) <=> ?[W]: (ssList(W) & app(V2, W)=U2))))).
% 24.18/3.48 fof(ax60, axiom, cyclefreeP(nil)).
% 24.18/3.48 fof(ax83, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => (nil=app(U2, V2) <=> (nil=V2 & nil=U2))))).
% 24.18/3.48 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X]: (ssList(X) => (nil!=W2 | (V2!=X | (U2!=W2 | ![Y]: (ssItem(Y) => ![Z]: (ssList(Z) => ![X1]: (ssList(X1) => (app(app(Z, cons(Y, nil)), X1)!=U2 | (~memberP(Z, Y) & ~memberP(X1, Y)))))))))))))).
% 24.18/3.48
% 24.18/3.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 24.18/3.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 24.18/3.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 24.18/3.48 fresh(y, y, x1...xn) = u
% 24.18/3.48 C => fresh(s, t, x1...xn) = v
% 24.18/3.48 where fresh is a fresh function symbol and x1..xn are the free
% 24.18/3.48 variables of u and v.
% 24.18/3.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 24.18/3.48 input problem has no model of domain size 1).
% 24.18/3.48
% 24.18/3.48 The encoding turns the above axioms into the following unit equations and goals:
% 24.18/3.48
% 24.18/3.48 Axiom 1 (co1_2): u = w.
% 24.18/3.48 Axiom 2 (co1_1): nil = w.
% 24.18/3.48 Axiom 3 (ax60): cyclefreeP(nil) = true2.
% 24.18/3.48 Axiom 4 (ax2): ssItem(u2) = true2.
% 24.18/3.48 Axiom 5 (co1_4): ssItem(y) = true2.
% 24.18/3.48 Axiom 6 (co1_5): ssList(u) = true2.
% 24.18/3.48 Axiom 7 (co1_10): ssList(x1) = true2.
% 24.18/3.48 Axiom 8 (co1_9): ssList(z) = true2.
% 24.18/3.48 Axiom 9 (ax4): fresh276(X, X, Y) = true2.
% 24.18/3.48 Axiom 10 (ax83_2): fresh117(X, X, Y) = Y.
% 24.18/3.48 Axiom 11 (ax83_1): fresh115(X, X, Y) = Y.
% 24.18/3.48 Axiom 12 (ax45): fresh57(X, X, Y) = true2.
% 24.18/3.48 Axiom 13 (ax28): fresh7(X, X, Y) = Y.
% 24.18/3.48 Axiom 14 (ax5_2): fresh274(X, X, Y, Z) = true2.
% 24.18/3.48 Axiom 15 (ax5_1): fresh272(X, X, Y, Z) = Y.
% 24.18/3.48 Axiom 16 (ax16): fresh76(X, X, Y, Z) = ssList(cons(Z, Y)).
% 24.18/3.48 Axiom 17 (ax16): fresh75(X, X, Y, Z) = true2.
% 24.18/3.48 Axiom 18 (ax26): fresh72(X, X, Y, Z) = ssList(app(Y, Z)).
% 24.18/3.48 Axiom 19 (ax26): fresh71(X, X, Y, Z) = true2.
% 24.18/3.48 Axiom 20 (ax4): fresh59(X, X, Y, Z) = singletonP(Y).
% 24.18/3.48 Axiom 21 (ax45): fresh57(ssList(X), true2, X) = frontsegP(X, nil).
% 24.18/3.48 Axiom 22 (ax5_2): fresh38(X, X, Y, Z) = ssList(w11(Y, Z)).
% 24.18/3.48 Axiom 23 (ax83_1): fresh21(X, X, Y, Z) = nil.
% 24.18/3.48 Axiom 24 (ax83_2): fresh20(X, X, Y, Z) = nil.
% 24.18/3.48 Axiom 25 (ax28): fresh7(ssList(X), true2, X) = app(nil, X).
% 24.18/3.48 Axiom 26 (ax5_1): fresh39(X, X, Y, Z) = app(Z, w11(Y, Z)).
% 24.18/3.48 Axiom 27 (ax4): fresh275(X, X, Y, Z) = fresh276(cons(Z, nil), Y, Y).
% 24.18/3.48 Axiom 28 (ax5_2): fresh273(X, X, Y, Z) = fresh274(ssList(Y), true2, Y, Z).
% 24.18/3.48 Axiom 29 (ax5_1): fresh271(X, X, Y, Z) = fresh272(ssList(Y), true2, Y, Z).
% 24.18/3.48 Axiom 30 (ax83_2): fresh116(X, X, Y, Z) = fresh117(nil, app(Y, Z), Z).
% 24.18/3.48 Axiom 31 (ax83_1): fresh114(X, X, Y, Z) = fresh115(nil, app(Y, Z), Y).
% 24.18/3.48 Axiom 32 (ax16): fresh76(ssList(X), true2, X, Y) = fresh75(ssItem(Y), true2, X, Y).
% 24.18/3.48 Axiom 33 (ax26): fresh72(ssList(X), true2, Y, X) = fresh71(ssList(Y), true2, Y, X).
% 24.18/3.48 Axiom 34 (ax4): fresh275(ssList(X), true2, X, Y) = fresh59(ssItem(Y), true2, X, Y).
% 24.18/3.48 Axiom 35 (ax83_1): fresh114(ssList(X), true2, Y, X) = fresh21(ssList(Y), true2, Y, X).
% 24.18/3.48 Axiom 36 (ax83_2): fresh116(ssList(X), true2, Y, X) = fresh20(ssList(Y), true2, Y, X).
% 24.18/3.48 Axiom 37 (ax5_2): fresh273(frontsegP(X, Y), true2, X, Y) = fresh38(ssList(Y), true2, X, Y).
% 24.18/3.48 Axiom 38 (ax5_1): fresh271(frontsegP(X, Y), true2, X, Y) = fresh39(ssList(Y), true2, X, Y).
% 24.18/3.48 Axiom 39 (co1): app(app(z, cons(y, nil)), x1) = u.
% 24.18/3.48
% 24.18/3.48 Lemma 40: nil = u.
% 24.18/3.48 Proof:
% 24.18/3.48 nil
% 24.18/3.48 = { by axiom 2 (co1_1) }
% 24.18/3.48 w
% 24.18/3.48 = { by axiom 1 (co1_2) R->L }
% 24.18/3.48 u
% 24.18/3.48
% 24.18/3.48 Lemma 41: ssItem(u2) = cyclefreeP(nil).
% 24.18/3.48 Proof:
% 24.18/3.48 ssItem(u2)
% 24.18/3.48 = { by axiom 4 (ax2) }
% 24.18/3.48 true2
% 24.18/3.48 = { by axiom 3 (ax60) R->L }
% 24.18/3.48 cyclefreeP(nil)
% 24.18/3.48
% 24.18/3.48 Lemma 42: ssItem(y) = ssItem(u2).
% 24.18/3.48 Proof:
% 24.18/3.48 ssItem(y)
% 24.18/3.48 = { by axiom 5 (co1_4) }
% 24.18/3.48 true2
% 24.18/3.48 = { by axiom 3 (ax60) R->L }
% 24.18/3.48 cyclefreeP(nil)
% 24.18/3.48 = { by lemma 41 R->L }
% 24.18/3.48 ssItem(u2)
% 24.18/3.48
% 24.18/3.48 Lemma 43: ssList(z) = ssItem(u2).
% 24.18/3.48 Proof:
% 24.18/3.48 ssList(z)
% 24.18/3.48 = { by axiom 8 (co1_9) }
% 24.18/3.48 true2
% 24.18/3.48 = { by axiom 3 (ax60) R->L }
% 24.18/3.48 cyclefreeP(nil)
% 24.18/3.48 = { by lemma 41 R->L }
% 24.18/3.48 ssItem(u2)
% 24.18/3.48
% 24.18/3.48 Lemma 44: ssList(x1) = ssItem(u2).
% 24.18/3.48 Proof:
% 24.18/3.48 ssList(x1)
% 24.18/3.48 = { by axiom 7 (co1_10) }
% 24.18/3.48 true2
% 24.18/3.48 = { by axiom 3 (ax60) R->L }
% 24.18/3.48 cyclefreeP(nil)
% 24.18/3.48 = { by lemma 41 R->L }
% 24.18/3.48 ssItem(u2)
% 24.18/3.48
% 24.18/3.48 Lemma 45: ssList(u) = ssItem(u2).
% 24.18/3.48 Proof:
% 24.18/3.48 ssList(u)
% 24.18/3.48 = { by axiom 6 (co1_5) }
% 24.18/3.48 true2
% 24.18/3.48 = { by axiom 3 (ax60) R->L }
% 24.18/3.48 cyclefreeP(nil)
% 24.18/3.48 = { by lemma 41 R->L }
% 24.18/3.48 ssItem(u2)
% 24.18/3.48
% 24.18/3.48 Lemma 46: ssList(cons(y, nil)) = ssItem(u2).
% 24.18/3.48 Proof:
% 24.18/3.48 ssList(cons(y, nil))
% 24.18/3.48 = { by lemma 40 }
% 24.18/3.48 ssList(cons(y, u))
% 24.18/3.48 = { by axiom 16 (ax16) R->L }
% 24.18/3.49 fresh76(ssItem(u2), ssItem(u2), u, y)
% 24.18/3.49 = { by lemma 45 R->L }
% 24.18/3.49 fresh76(ssList(u), ssItem(u2), u, y)
% 24.18/3.49 = { by lemma 41 }
% 24.18/3.49 fresh76(ssList(u), cyclefreeP(nil), u, y)
% 24.18/3.49 = { by axiom 3 (ax60) }
% 24.18/3.49 fresh76(ssList(u), true2, u, y)
% 24.18/3.49 = { by axiom 32 (ax16) }
% 24.18/3.49 fresh75(ssItem(y), true2, u, y)
% 24.18/3.49 = { by axiom 3 (ax60) R->L }
% 24.18/3.49 fresh75(ssItem(y), cyclefreeP(nil), u, y)
% 24.18/3.49 = { by lemma 41 R->L }
% 24.18/3.49 fresh75(ssItem(y), ssItem(u2), u, y)
% 24.18/3.49 = { by lemma 42 }
% 24.18/3.49 fresh75(ssItem(u2), ssItem(u2), u, y)
% 24.18/3.49 = { by axiom 17 (ax16) }
% 24.18/3.49 true2
% 24.18/3.49 = { by axiom 3 (ax60) R->L }
% 24.18/3.49 cyclefreeP(nil)
% 24.18/3.49 = { by lemma 41 R->L }
% 24.18/3.49 ssItem(u2)
% 24.18/3.49
% 24.18/3.49 Lemma 47: ssList(app(app(z, cons(y, nil)), x1)) = ssItem(u2).
% 24.18/3.49 Proof:
% 24.18/3.49 ssList(app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 39 (co1) }
% 24.18/3.49 ssList(u)
% 24.18/3.49 = { by lemma 45 }
% 24.18/3.49 ssItem(u2)
% 24.18/3.49
% 24.18/3.49 Lemma 48: frontsegP(x1, app(app(z, cons(y, nil)), x1)) = ssItem(u2).
% 24.18/3.49 Proof:
% 24.18/3.49 frontsegP(x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 39 (co1) }
% 24.18/3.49 frontsegP(x1, u)
% 24.18/3.49 = { by lemma 40 R->L }
% 24.18/3.49 frontsegP(x1, nil)
% 24.18/3.49 = { by axiom 21 (ax45) R->L }
% 24.18/3.49 fresh57(ssList(x1), true2, x1)
% 24.18/3.49 = { by axiom 3 (ax60) R->L }
% 24.18/3.49 fresh57(ssList(x1), cyclefreeP(nil), x1)
% 24.18/3.49 = { by lemma 41 R->L }
% 24.18/3.49 fresh57(ssList(x1), ssItem(u2), x1)
% 24.18/3.49 = { by lemma 44 }
% 24.18/3.49 fresh57(ssItem(u2), ssItem(u2), x1)
% 24.18/3.49 = { by axiom 12 (ax45) }
% 24.18/3.49 true2
% 24.18/3.49 = { by axiom 3 (ax60) R->L }
% 24.18/3.49 cyclefreeP(nil)
% 24.18/3.49 = { by lemma 41 R->L }
% 24.18/3.49 ssItem(u2)
% 24.18/3.49
% 24.18/3.49 Lemma 49: ssList(w11(x1, app(app(z, cons(y, nil)), x1))) = ssItem(u2).
% 24.18/3.49 Proof:
% 24.18/3.49 ssList(w11(x1, app(app(z, cons(y, nil)), x1)))
% 24.18/3.49 = { by axiom 22 (ax5_2) R->L }
% 24.18/3.49 fresh38(ssItem(u2), ssItem(u2), x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 47 R->L }
% 24.18/3.49 fresh38(ssList(app(app(z, cons(y, nil)), x1)), ssItem(u2), x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 41 }
% 24.18/3.49 fresh38(ssList(app(app(z, cons(y, nil)), x1)), cyclefreeP(nil), x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 3 (ax60) }
% 24.18/3.49 fresh38(ssList(app(app(z, cons(y, nil)), x1)), true2, x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 37 (ax5_2) R->L }
% 24.18/3.49 fresh273(frontsegP(x1, app(app(z, cons(y, nil)), x1)), true2, x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 3 (ax60) R->L }
% 24.18/3.49 fresh273(frontsegP(x1, app(app(z, cons(y, nil)), x1)), cyclefreeP(nil), x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 41 R->L }
% 24.18/3.49 fresh273(frontsegP(x1, app(app(z, cons(y, nil)), x1)), ssItem(u2), x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 48 }
% 24.18/3.49 fresh273(ssItem(u2), ssItem(u2), x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 28 (ax5_2) }
% 24.18/3.49 fresh274(ssList(x1), true2, x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 3 (ax60) R->L }
% 24.18/3.49 fresh274(ssList(x1), cyclefreeP(nil), x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 41 R->L }
% 24.18/3.49 fresh274(ssList(x1), ssItem(u2), x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 44 }
% 24.18/3.49 fresh274(ssItem(u2), ssItem(u2), x1, app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 14 (ax5_2) }
% 24.18/3.49 true2
% 24.18/3.49 = { by axiom 3 (ax60) R->L }
% 24.18/3.49 cyclefreeP(nil)
% 24.18/3.49 = { by lemma 41 R->L }
% 24.18/3.49 ssItem(u2)
% 24.18/3.49
% 24.18/3.49 Goal 1 (ax39): singletonP(nil) = true2.
% 24.18/3.49 Proof:
% 24.18/3.49 singletonP(nil)
% 24.18/3.49 = { by lemma 40 }
% 24.18/3.49 singletonP(u)
% 24.18/3.49 = { by axiom 20 (ax4) R->L }
% 24.18/3.49 fresh59(ssItem(u2), ssItem(u2), u, y)
% 24.18/3.49 = { by lemma 42 R->L }
% 24.18/3.49 fresh59(ssItem(y), ssItem(u2), u, y)
% 24.18/3.49 = { by lemma 41 }
% 24.18/3.49 fresh59(ssItem(y), cyclefreeP(nil), u, y)
% 24.18/3.49 = { by axiom 3 (ax60) }
% 24.18/3.49 fresh59(ssItem(y), true2, u, y)
% 24.18/3.49 = { by axiom 34 (ax4) R->L }
% 24.18/3.49 fresh275(ssList(u), true2, u, y)
% 24.18/3.49 = { by axiom 3 (ax60) R->L }
% 24.18/3.49 fresh275(ssList(u), cyclefreeP(nil), u, y)
% 24.18/3.49 = { by lemma 41 R->L }
% 24.18/3.49 fresh275(ssList(u), ssItem(u2), u, y)
% 24.18/3.49 = { by lemma 45 }
% 24.18/3.49 fresh275(ssItem(u2), ssItem(u2), u, y)
% 24.18/3.49 = { by axiom 39 (co1) R->L }
% 24.18/3.49 fresh275(ssItem(u2), ssItem(u2), app(app(z, cons(y, nil)), x1), y)
% 24.18/3.49 = { by axiom 27 (ax4) }
% 24.18/3.49 fresh276(cons(y, nil), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 10 (ax83_2) R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 39 (co1) }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), u, cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 40 R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), nil, cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 23 (ax83_1) R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 41 }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(cyclefreeP(nil), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 3 (ax60) }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(true2, ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 19 (ax26) R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(fresh71(ssItem(u2), ssItem(u2), z, cons(y, nil)), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 43 R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(fresh71(ssList(z), ssItem(u2), z, cons(y, nil)), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 41 }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(fresh71(ssList(z), cyclefreeP(nil), z, cons(y, nil)), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 3 (ax60) }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(fresh71(ssList(z), true2, z, cons(y, nil)), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 33 (ax26) R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(fresh72(ssList(cons(y, nil)), true2, z, cons(y, nil)), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 3 (ax60) R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(fresh72(ssList(cons(y, nil)), cyclefreeP(nil), z, cons(y, nil)), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 41 R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(fresh72(ssList(cons(y, nil)), ssItem(u2), z, cons(y, nil)), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 46 }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(fresh72(ssItem(u2), ssItem(u2), z, cons(y, nil)), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 18 (ax26) }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(ssList(app(z, cons(y, nil))), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 41 }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(ssList(app(z, cons(y, nil))), cyclefreeP(nil), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 3 (ax60) }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh21(ssList(app(z, cons(y, nil))), true2, app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 35 (ax83_1) R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssList(w11(x1, app(app(z, cons(y, nil)), x1))), true2, app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 3 (ax60) R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssList(w11(x1, app(app(z, cons(y, nil)), x1))), cyclefreeP(nil), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 41 R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssList(w11(x1, app(app(z, cons(y, nil)), x1))), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 49 }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), w11(x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 13 (ax28) R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh7(ssItem(u2), ssItem(u2), w11(x1, app(app(z, cons(y, nil)), x1)))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 49 R->L }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh7(ssList(w11(x1, app(app(z, cons(y, nil)), x1))), ssItem(u2), w11(x1, app(app(z, cons(y, nil)), x1)))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by lemma 41 }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh7(ssList(w11(x1, app(app(z, cons(y, nil)), x1))), cyclefreeP(nil), w11(x1, app(app(z, cons(y, nil)), x1)))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 3 (ax60) }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh7(ssList(w11(x1, app(app(z, cons(y, nil)), x1))), true2, w11(x1, app(app(z, cons(y, nil)), x1)))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.49 = { by axiom 25 (ax28) }
% 24.18/3.49 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), app(nil, w11(x1, app(app(z, cons(y, nil)), x1)))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 40 }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), app(u, w11(x1, app(app(z, cons(y, nil)), x1)))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 39 (co1) R->L }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), app(app(app(z, cons(y, nil)), x1), w11(x1, app(app(z, cons(y, nil)), x1)))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 26 (ax5_1) R->L }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh39(ssItem(u2), ssItem(u2), x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 47 R->L }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh39(ssList(app(app(z, cons(y, nil)), x1)), ssItem(u2), x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 41 }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh39(ssList(app(app(z, cons(y, nil)), x1)), cyclefreeP(nil), x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 3 (ax60) }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh39(ssList(app(app(z, cons(y, nil)), x1)), true2, x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 38 (ax5_1) R->L }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh271(frontsegP(x1, app(app(z, cons(y, nil)), x1)), true2, x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 3 (ax60) R->L }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh271(frontsegP(x1, app(app(z, cons(y, nil)), x1)), cyclefreeP(nil), x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 41 R->L }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh271(frontsegP(x1, app(app(z, cons(y, nil)), x1)), ssItem(u2), x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 48 }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh271(ssItem(u2), ssItem(u2), x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 29 (ax5_1) }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh272(ssList(x1), true2, x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 3 (ax60) R->L }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh272(ssList(x1), cyclefreeP(nil), x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 41 R->L }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh272(ssList(x1), ssItem(u2), x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 44 }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), fresh272(ssItem(u2), ssItem(u2), x1, app(app(z, cons(y, nil)), x1))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 15 (ax5_1) }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh114(ssItem(u2), ssItem(u2), app(z, cons(y, nil)), x1), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 31 (ax83_1) }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh115(nil, app(app(z, cons(y, nil)), x1), app(z, cons(y, nil))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 40 }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh115(u, app(app(z, cons(y, nil)), x1), app(z, cons(y, nil))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 39 (co1) R->L }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), fresh115(app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1), app(z, cons(y, nil))), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 11 (ax83_1) }
% 24.18/3.50 fresh276(fresh117(app(app(z, cons(y, nil)), x1), app(z, cons(y, nil)), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 39 (co1) }
% 24.18/3.50 fresh276(fresh117(u, app(z, cons(y, nil)), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 40 R->L }
% 24.18/3.50 fresh276(fresh117(nil, app(z, cons(y, nil)), cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 30 (ax83_2) R->L }
% 24.18/3.50 fresh276(fresh116(ssItem(u2), ssItem(u2), z, cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 46 R->L }
% 24.18/3.50 fresh276(fresh116(ssList(cons(y, nil)), ssItem(u2), z, cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 41 }
% 24.18/3.50 fresh276(fresh116(ssList(cons(y, nil)), cyclefreeP(nil), z, cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 3 (ax60) }
% 24.18/3.50 fresh276(fresh116(ssList(cons(y, nil)), true2, z, cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 36 (ax83_2) }
% 24.18/3.50 fresh276(fresh20(ssList(z), true2, z, cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 3 (ax60) R->L }
% 24.18/3.50 fresh276(fresh20(ssList(z), cyclefreeP(nil), z, cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 41 R->L }
% 24.18/3.50 fresh276(fresh20(ssList(z), ssItem(u2), z, cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 43 }
% 24.18/3.50 fresh276(fresh20(ssItem(u2), ssItem(u2), z, cons(y, nil)), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 24 (ax83_2) }
% 24.18/3.50 fresh276(nil, app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by lemma 40 }
% 24.18/3.50 fresh276(u, app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 39 (co1) R->L }
% 24.18/3.50 fresh276(app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1), app(app(z, cons(y, nil)), x1))
% 24.18/3.50 = { by axiom 9 (ax4) }
% 24.18/3.50 true2
% 24.18/3.50 % SZS output end Proof
% 24.18/3.50
% 24.18/3.50 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------